Glasgow Mathematical Journal



Compact well-bounded operators


Cheng  Qingping  a1 1 and Ian  Doust  a2 2
a1 School of Mathematical and Physical Sciences, Murdoch University, Murdoch, WA 6150, Australia e-mail: cheng@prodigal.murdoch.edu.au
a2 School of Mathematics, University of New South Wales, Sydney, NSW 2052, Australia e-mail: i.doust@unsw.edu.au

Every compact well-bounded operator has a representation as a linear combination of disjoint projections reminiscent of the representation of compact self-adjoint operators. In this note we show that the converse of this result holds, thus characterizing compact well-bounded operators. We also apply this result to study compact well-bounded operators on some special classes of Banach spaces such as hereditarily indecomposable spaces and certain spaces constructed by G. Pisier.



Footnotes

1 Some of this work forms part of the PhD research of the first author undertaken at Murdoch University under the supervision of Ken Harrison.

2 The research of the second author was supported by the Australian Research Council.